Trairashika: Rule Of Three | Class 8 Maths Book 1 Ch 7

📘 Class 8 · Ganita Prakash Book 1Ch 7 · Proportional Reasoning-1Post 6 / 9⏱ 25–30 min

Trairashika: Rule Of Three 🔺

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

3 : 5 :: x : 40 mein x?
175 ÷ 50?
Proportion ka matlab (Post 4 — Proportion Kya Hai? (:: Ka Matlab))?

Answers dekho

24
3.5
Do ratio barabar

Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 4 — Proportion Kya Hai? (:: Ka Matlab) dekh lijiye.

— 📌 charumam.com

🎬 Kahani: Halwai Ki Shaadi Wali Mushkil

Ramesh halwai: “50 mehmaan ke liye 8 kg aaloo lagte hain.” Aaj shaadi mein 175 mehmaan! 🍛

Unka beta: “Papa, 175 − 50 = 125 zyada log, to 125 kg aur?” Halwai hans pade: “Pagle, poore mohalle ki sabzi ban jaayegi!”

Sahi jawab ka 1500 saal purana tareeka: Trairashika, teen jaani maatra se chauthi.

— 📌 charumam.com

📖 Concept: Trairashika = Teen Se Chautha (Proportion Ka Hathiyaar)

💡 Is post ki ek badi baat: Teen jaani maatraein: pramana (jaani maatra, 50 log), phala (uska nateeja, 8 kg), ichchha (jo chahiye, 175 log). Agar dono proportional hain to ichchha-phala = phala × ichchha ÷ pramana.

Step 1: Pehle: kya yeh proportional hai?

Log double → aaloo double? Haan (har mehmaan utna hi khaata). Tabhi trairashika lagta.

WHY pehle check? Rule of three sirf proportional (same factor) rishte pe chalta. Varna galat jawab (Post 1 — Proportional Badlaav Kya Hai?).

Step 2: Tareeka 1: Unitary (ek ke liye)

50 log → 8 kg. 1 log → 8/50 = 0.16 kg. 175 log → 0.16 × 175 = 28 kg.

Kab aasaan: jab ek-ek ka hisaab saaf ho (per kg daam, per ghanta).

Step 3: Tareeka 2: Factor (kitna guna)

175 ÷ 50 = 3.5 guna log → aaloo bhi 3.5 guna: 8 × 3.5 = 28 kg.

Kab aasaan: jab factor saaf ho (2, 3.5, 10). Yahi hamara central idea: same factor!

Step 4: Tareeka 3: Proportion / cross

50 : 8 :: 175 : x → 50x = 8 × 175 = 1400 → x = 28.

WHY formula? x = 8 × 175 ÷ 50 = phala × ichchha ÷ pramana. Cross product ka hi roop! Kab aasaan: ajeeb numbers.

Step 5: Itihaas

Aryabhata (Aryabhatiya, lagbhag 499 CE) mein trairashika ka niyam hai; baad mein Brahmagupta, Bhaskara ne bhi likha. Arab aur Europe tak “Rule of Three” naam se pahuncha, vyapaariyon ka sabse pyaara niyam! 🏛️

🪜 Atak Gaye? Aise Socho

Teen maatraein pehchaano: pramana, phala, ichchha.
Proportional hai? (double → double?)
Factor ya unitary chuno.
Guna karo.
Check: kya jawab samajhdaar? (zyada log → zyada aaloo)

— 📌 charumam.com

🔐 Deep Concept: Teen Tareeke, Ek Hi Sach: Factor Dono Taraf

Unitary: pehle ÷ 50, phir × 175. Factor: × (175/50). Cross: × 175 ÷ 50. Teeno mein bas order alag, kaam same: aaloo ko 175/50 se guna.

Kyun? Proportional rishta matlab ek line (Post 3 — Ratio Ka Simplest Form ki family): aaloo = 0.16 × log. Constant 0.16 hi “unit rate” hai, aur 175/50 “beech ka factor”.

Kab FAIL? Agar rishta proportional nahi: “4 mazdoor 6 din, 8 mazdoor?” Zyada mazdoor = kam din (ulta). Ya taxi: fixed ₹40 + per km (Post 9 — Proportion Ke Tricky Sawaal). Pehle hamesha poochho: “double → double?”

Unifying idea: trairashika proportion ka hathiyaar hai, jo same factor wale rishte pe chalta. 🎯

sirf charumam.com readers ke liye 🔐

✏️ Solved Examples

Example 1 (Easy): 6 m kapda ₹840. 15 m?

Factor 2.5 → ₹2100.

Check: per m ₹140 × 15 = 2100 ✅

📌 charumam.com

Example 2 (Medium): Car 12 litre mein 210 km. 20 litre?

Per litre 17.5 → 350 km.

Check: 12 : 210 :: 20 : 350 → 4200 = 4200 ✅

📌 charumam.com

Example 3 (NCERT style): 3 kg aata se 45 roti. 160 roti ke liye?

Per kg 15 roti → 160/15 = 10 2/3 kg (≈ 10.67).

Check: 10 2/3 × 15 = 160 ✅

📌 charumam.com

Halwai ka jawab: 28 kg (3.5 guna). Bete ka “125 kg aur” farak wali soch thi; sahi soch guna wali! 🍛

— 📌 charumam.com

🏠 Trairashika Roz Ki Zindagi Mein

🛒 Dukaan: 250 g ka daam se 1.5 kg.
🍳 Recipe scale: 4 logon se 10 logon tak.
⛽ Petrol: mileage se doori.
💱 Currency: 1 dollar ka rate se 250 dollar.
🗺️ Map: scale se asli doori.

Purane vyapaari bina calculator ke trairashika se hi hazaaron ka hisaab karte the. Aap bhi!

— 📌 charumam.com

🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Ek ka hisaab saaf	✅ Unitary	₹/m
Factor saaf	✅ Kitna guna	× 3.5
Ajeeb numbers	✅ Cross	x = bc/a
Rishta ulta (mazdoor-din)	❌ Seedha rule nahi	Inverse
Fixed + per unit	❌ Seedha nahi	Pehle fixed hatao

— 📌 charumam.com

❌→✅ Worked Mistake

Sawaal: 4 pen ₹60. 10 pen?

❌ Galat: “6 pen zyada, to ₹66” (farak jod diya) ya “60 × 4 ÷ 10 = ₹24” (ulta).

✅ Sahi: 60 × 10 ÷ 4 = ₹150. Check: per pen ₹15 × 10 = 150 ✅; zyada pen → zyada daam ✅

🧠 Rule of thumb: Phala × ichchha ÷ pramana. Jawab ka samajhdaar check: zyada maango, zyada aaye.

sirf charumam.com pe milenge!

📝 10 MCQs

Q1. 50 log 8 kg, 175 log?

(a) 28 kg

(b) 133 kg

(c) 25 kg

(d) 11.5 kg

Solution dekho

Sahi jawab: (a)

(a) sahi: 175 ÷ 50 = 3.5, 8 × 3.5 = 28 kg ✅
(b) galat: 133 mein 125 jod diya: farak wali soch.
(c) galat: 25 kg ka factor galat liya.
(d) galat: 11.5 mein 3.5 jod diya, guna nahi.

Q2. Pramana kya hai?

(a) Jaani maatra

(b) Jawab

(c) Chahiye wali

(d) Factor

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 50 log jaisa ✅
(b) galat: Woh ichchha-phala hai.
(c) galat: Woh ichchha hai, isliye yeh galat.
(d) galat: Factor alag cheez, isliye yeh galat.

Q3. 4 pen ₹60, 10 pen?

(a) ₹150

(b) ₹66

(c) ₹24

(d) ₹240

Solution dekho

Sahi jawab: (a)

(a) sahi: Bilkul sahi jawab: 15 × 10 ✅
(b) galat: Farak jod diya, isliye yeh galat.
(c) galat: Ulta kiya, isliye yeh galat.
(d) galat: 4 se guna kiya, isliye yeh galat.

Q4. Trairashika kab nahi?

(a) Ulta rishta

(b) Seedha rishta

(c) Kabhi nahi

(d) Hamesha

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: Mazdoor-din ✅
(b) galat: Seedhe mein chalta, isliye yeh galat.
(c) galat: Kahin fail hota, isliye yeh galat.
(d) galat: Hamesha nahi, isliye yeh galat.

Q5. 6 m ₹840, 15 m?

(a) ₹2100

(b) ₹1400

(c) ₹2520

(d) ₹336

Solution dekho

Sahi jawab: (a)

(a) sahi: Bilkul sahi jawab: × 2.5 ✅
(b) galat: 10 m ka daam, isliye yeh galat.
(c) galat: 18 m ka daam, isliye yeh galat.
(d) galat: Ulta bhaag, isliye yeh galat.

Q6. Aryabhatiya lagbhag?

(a) 499 CE

(b) 1499 CE

(c) 100 BCE

(d) 1900 CE

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: Aryabhata ✅
(b) galat: Itna baad nahi, isliye yeh galat.
(c) galat: Itna pehle nahi, isliye yeh galat.
(d) galat: Bahut baad, isliye yeh galat.

Q7. Teeno tareeke mein common?

(a) Phala × ichchha/pramana

(b) Jod

(c) Ghatao

(d) Kuch nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: Same factor ✅
(b) galat: Jod nahi chalta, isliye yeh galat.
(c) galat: Ghatao nahi, isliye yeh galat.
(d) galat: Sab mein same, isliye yeh galat.

Q8. Taxi ₹40 + ₹12/km: seedha rule?

(a) Nahi

(b) Haan

(c) Hamesha

(d) Sirf 1 km

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: Fixed hissa ✅
(b) galat: Double km ≠ double kiraya.
(c) galat: Proportional nahi, isliye yeh galat.
(d) galat: Kisi pe nahi, isliye yeh galat.

Q9. 12 l 210 km, 20 l?

(a) 350 km

(b) 218 km

(c) 126 km

(d) 420 km

Solution dekho

Sahi jawab: (a)

(a) sahi: 210 ÷ 12 = 17.5 km/l × 20 = 350 ✅
(b) galat: 218 mein farak 8 jod diya.
(c) galat: 126 mein ulta (12/20) factor lagaya.
(d) galat: 420 to 24 litre ka jawab hai.

Q10. Check kya karein?

(a) Zyada → zyada

(b) Jawab chhota

(c) Hamesha whole

(d) Kuch nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: Samajhdaar check ✅
(b) galat: Zaroori nahi, isliye yeh galat.
(c) galat: Fraction ho sakta, isliye yeh galat.
(d) galat: Check zaroori, isliye yeh galat.

— 📌 charumam.com

❓ FAQs (Bachchon Ke Asli Sawaal)

1. Trairashika ka matlab?

Tri (teen) + raashi (maatra): teen maatraon ka niyam.

2. Rule of Five?

Do baar trairashika: jaise log aur din dono badlein.

3. Inverse proportion?

Ek badhe, doosra ghate (guna constant). Aage padhenge.

4. Fraction jawab?

Chalta hai: 10 2/3 kg.

5. Unitary vs factor?

Jo aasaan lage; dono same.

6. Aage?

Barabar nahi, ratio mein baantna: Post 7 — Barabar Nahi, Ratio Mein Hissa.

— 📌 charumam.com

🏋️ Practice Zone (12 Sawaal)

Q1. Easy 5 kg chawal ₹320. 8 kg?

Solution dekho

₹512. Check: 64 × 8 ✅

Q2. Easy 2 ghante 90 km. 5 ghante?

Solution dekho

225 km. Check ✅

Q3. Easy 12 copies ₹216. 20?

Solution dekho

₹360. Check: 18 × 20 ✅

Q4. Easy 1 cm = 25 km. 7.2 cm?

Solution dekho

180 km. Check ✅

Q5. Medium 250 g ₹45. 1.5 kg?

Solution dekho

× 6 → ₹270. Check ✅

Q6. Medium 4 logon ke liye 300 g dal. 10?

Solution dekho

750 g. Check ✅

Q7. Medium ₹1 = 0.012 dollar. ₹4500?

Solution dekho

54 dollar. Check ✅

Q8. Medium 8 litre paint 120 sq m. 300 sq m?

Solution dekho

20 litre. Check ✅

Q9. NCERT style Taxi ₹40 + ₹12/km. 15 km?

Solution dekho

₹220 (seedha rule nahi). Check: 40 + 180 ✅

Q10. NCERT style 3 kg aata 45 roti. 100 roti?

Solution dekho

6 2/3 kg. Check: × 15 = 100 ✅

Q11. NCERT style Printer 6 min mein 84 page. 210 page?

Solution dekho

15 min. Check ✅

Q12. NCERT style 6 mazdoor 10 din. 12 mazdoor? Trairashika seedha?

Solution dekho

Nahi, ulta: 5 din. Check: 60 mazdoor-din ✅

Answer Key — charumam.com exclusive

🧠 HOTS (Sochne Wale Sawaal)

Q1. 15 log 3 din mein 90 kg khaate. 20 log 6 din?

Solution dekho

Per log-din 2 kg → 240 kg. Check ✅

Q2. Ghadi har din 3 min tez. 2 hafte?

Solution dekho

42 min. Check ✅

Q3. Kya umar aur height mein trairashika?

Solution dekho

Nahi, proportional nahi. Check ✅

Q4. 24 ₹ mein 9 aam. ₹40 mein?

Solution dekho

15. Check: 24 : 9 :: 40 : 15 ✅

sirf charumam.com pe milenge!

🏆 Olympiad Corner

Q1. 7 pen ₹91. 11?

Solution dekho

₹143.

Q2. 45 km 1.5 ghante. 2.5?

Solution dekho

75 km.

Q3. 18 m kapda 6 kurta. 45 m?

Solution dekho

15.

Q4. 600 g ₹84. 1 kg?

Solution dekho

₹140.

sirf charumam.com readers ke liye 🔐

💗 CharuMam Motivation

Aryabhata ka niyam, aaj aapki jeb mein! Halwai ho ya dukaandaar, trairashika hamesha saath. 🔺

— 📌 charumam.com

🟢 Master Recap

💡 Chaabi: Teen jaani maatraein: pramana (jaani maatra, 50 log), phala (uska nateeja, 8 kg), ichchha (jo chahiye, 175 log). Agar dono proportional hain to ichchha-phala = phala × ichchha ÷ pramana.
Pramana, phala, ichchha.
Pehle check: proportional?
Unitary, factor, cross.
Phala × ichchha ÷ pramana.
Ulta ya fixed rishta: seedha nahi.
Samajhdaar check.

— charumam.com 🎯

👉 Aage Kya?

Nana ji ke kanche 3 : 2 mein kaise baante? Post 7 — Barabar Nahi, Ratio Mein Hissa.

← Pichla: Post 5 — Ratio Se Tulna: Strong Ya Light?📚 Chapter 7 ke saare posts Agla: Post 7 — Barabar Nahi, Ratio Mein Hissa →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Halwai Ki Shaadi Wali Mushkil

📖 Concept: Trairashika = Teen Se Chautha (Proportion Ka Hathiyaar)

Step 1: Pehle: kya yeh proportional hai?

Step 2: Tareeka 1: Unitary (ek ke liye)

Step 3: Tareeka 2: Factor (kitna guna)

Step 4: Tareeka 3: Proportion / cross

Step 5: Itihaas

🪜 Atak Gaye? Aise Socho

🔐 Deep Concept: Teen Tareeke, Ek Hi Sach: Factor Dono Taraf

✏️ Solved Examples

🏠 Trairashika Roz Ki Zindagi Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

You may also like